1. Technical Field
The present disclosure relates to telecommunication and, more specifically, to wireless communication transmit diversity decoding.
2. Description of Related Art
The new 4G wireless technology standard termed Long Term Evolution-Advanced (LTE-A) utilizes the well-known modulation scheme known as orthogonal frequency division multiple access (OFDMA). It is a multicarrier technique in which the transmit spectrum is divided into K orthogonal subcarriers equally spaced in frequency. The method has been used for many years in both wireline broadband communications and wireless local area networks (WLAN). LTE-A provides a minimum of 1000 Mbps throughput in the downlink (DL) and 500 Mbps in the uplink (UL). The spectral bandwidth for LTE-A is 100 MHz, using up to five component carriers each with a component bandwidth of up to 20 MHz. LTE-A also includes support for both frequency domain duplexing and time domain duplexing.
LTE-A also employs multiple antenna methods such as spatial multiplexing and transmit diversity. Spatial multiplexing (SM) is a multiple-input-multiple-output system (MIMO) formulation enabled by configuring multiple antennas separated in space. The spatially separated antennas provide separate and distinct transmission channels allowing the transmitter-receiver pair to extract independent signals from each channel while cancelling interference from the other transmission paths. When combined, OFDMA and MIMO-SM provide orthogonality in both frequency and space. LTE-A supports up to eight antennas per modem.
Another application of a MIMO system configuration is to provide transmit diversity. Transmit diversity, as the name implies, enables the transmitter to send multiple copies of the same signal (or processed variations of the same signal) over several of the separate antenna paths available when the transmitting and receiving modems have more than one antenna. Wireless communications systems must contend with radio signal propagation impairments that include multipath fading, noise, and interference. Multipath fading results from a transmitted radio signal transversing many different paths from a transmitting antenna to a receiving antenna as a result of reflections from both man-made and natural environmental objects. The multiple reflected signals (including a possible line-of-sight signal) combine at the receiver to form a transmission path impulse response (with an associated transmission path frequency response). Depending on the characteristics of this response, it is possible for parts of the transmission channel to have deep nulls, which can be time-varying as a result of movement of the transmitter, the receiver, and the objects causing reflections. A wireless MIMO system has different transmission paths for its spatially separated antennas. The transmission path diversity increases the probability that the transmit signal can be correctly received at the decoder while some of the transmission paths are subject to harsh attenuation as a result of the multipath fading problem.
FIGS. 4-7 show some examples of MIMO system configuration. More specifically, FIG. 4 shows a single-input-single-output (SISO) system in a single cell for a single user between an LTE base station 410 and a user equipment 420. FIG. 5 shows a multiple input, single output (MISO) system in a single cell for a single user between an LTE base station 510 and a user equipment 520. FIG. 6 shows a MIMO system in a single cell for a single user between an LTE base station 610 and a user equipment 620. FIG. 7 shows a MIMO system, or interference, in a cooperative multi-cell environment for a single user between LTE base stations 710, 715 and user equipment 720, 725.
The description below provides background information on MIMO communications for OFDM.
Optimal multi-antenna formulation for OFDM spatial multiplexing, where there are M antenna to transmit signals and N antennas to receive signals, assumes that the duration of the time response of the channel is less than the OFDM cyclic prefix (CP), hence no inter-symbol interference (ISI), and is expressed as follows:r=Hy+n where:                H=M×N MIMO channel frequency response matrix (M being the number of transmit antennas, N being the number of receive antennas);        r=received frequency domain signal;        y=precoder frequency domain output signal;        n=noise; and        s=detected frequency domain signal.        
If OFDM, the FFT (receiver demodulator) and IFFT (transmit modulator) provide transformation of signals between the time domain and frequency domain. The MIMO channel formulation is used to model the channel response from the frequency domain signal in the transmitter to the frequency domain signal in the receiver.
Channel diagonalization via the well-known singular value decomposition (SVD) can be expressed as follows:H=SVD(H)=UDVH where U, V are unitary eigenvector matrices and D is a diagonal eigenvalue matrix. Several well established methods and algorithms are available in text books and papers to calculate the SVD.
Further, with respect to the following expression:r=UDVHy+n it is assigned that y=Vx and s=UHr as the (modified) transmit and receive signals, respectively, where x is the precoder input signal. This provides the following:S=UHr=UHUDVHVx+UHn s=Dx+UHn 
Since D is diagonal, the antenna channels are now orthogonalized and spatial interference is removed from the received signal s. The singular values are the square roots of the nonzero eigenvalues of HHH with rank≦min(M,N). Given that U is unitary, the noise variance of the orthogonalized system is unchanged with no noise enhancement. Accordingly, the optimal MIMO solution for spatial multiplexing can be expressed as follows:V=precoder,UH=equalizer
The description below provides background information on transmit diversity schemes.
Ordinarily, maximum ratio combining (MRC) receivers are used; however, in LTE space frequency block codes are used. A block code is defined for 2 transmit antennas and 4 transmit antennas, respectively, and the following pertains to the LTE block code definitions thereof.
In the case of 2 antenna ports, pεE {0,1}, the frequency domain output y(i)=[y(0)(i)y(1)(i)]T, where i=0, 1, . . . , Msymbap−1 is the carrier index, of the transmitter precoding operation is defined by the following expression:
      [                                                      y                              (                0                )                                      ⁡                          (                              2                ⁢                ⅈ                            )                                                                                      y                              (                1                )                                      ⁡                          (                              2                ⁢                ⅈ                            )                                                                                      y                              (                0                )                                      ⁡                          (                                                2                  ⁢                  ⅈ                                +                1                            )                                                                                      y                              (                1                )                                      ⁡                          (                                                2                  ⁢                  ⅈ                                +                1                            )                                            ]    =                    1                  2                    ⁡              [                                            1                                      0                                      j                                      0                                                          0                                                      -                1                                                    0                                      j                                                          0                                      1                                      0                                      j                                                          1                                      0                                                      -                j                                                    0                                      ]              ⁡          [                                                  Re              ⁡                              (                                                      x                                          (                      0                      )                                                        ⁡                                      (                    ⅈ                    )                                                  )                                                                                        Re              ⁡                              (                                                      x                                          (                      1                      )                                                        ⁡                                      (                    ⅈ                    )                                                  )                                                                                        Im              ⁡                              (                                                      x                                          (                      0                      )                                                        ⁡                                      (                    ⅈ                    )                                                  )                                                                                        Im              ⁡                              (                                                      x                                          (                      1                      )                                                        ⁡                                      (                    ⅈ                    )                                                  )                                                        ]      for i=0, 1, . . . , Msymblayer−1 with Msymbap=2Msymblayer, where Msymblayer is the number of symbols per layer, and Msymbap is the number of symbol per antenna port.
The superscript for y(p)( ) indicates the antenna port number {0,1}. The operators Re( ) and Im( ) refer to the real and imaginary components of the complex precoder input signal x(p)(i). For the case of two antenna ports, there are two input signals, and the span of the precoder covers two adjacent frequency domain carriers using two antenna ports. The transmit precoder generates the IFFT modulator input signal in the frequency domain.
The precoding operation can be rewritten showing permutation and modification of the two transmit symbols x(0)(i) and x(1)(i) on the two antenna ports using adjacent frequency carriers as follows:
      [                                                      y                              (                0                )                                      ⁡                          (                              2                ⁢                ⅈ                            )                                                                                      y                              (                1                )                                      ⁡                          (                              2                ⁢                ⅈ                            )                                                                                      y                              (                0                )                                      ⁡                          (                                                2                  ⁢                  ⅈ                                +                1                            )                                                                                      y                              (                1                )                                      ⁡                          (                                                2                  ⁢                  ⅈ                                +                1                            )                                            ]    =            1              2              ⁡          [                                                                  x                                  (                  0                  )                                            ⁡                              (                ⅈ                )                                                                                        -                              conj                ⁡                                  (                                                            x                                              (                        1                        )                                                              ⁡                                          (                      ⅈ                      )                                                        )                                                                                                                        x                                  (                  1                  )                                            ⁡                              (                ⅈ                )                                                                                        conj              ⁡                              (                                                      x                                          (                      0                      )                                                        ⁡                                      (                    ⅈ                    )                                                  )                                                        ]      where the conj( ) operator refers to the complex conjugate of x(p)(i).
In the case of 4 antenna ports, pε{0, 1, 2, 3}, the output y(i)=[y(0)(i)y(1)(i)y(2)(i)y(3)(i)]T, i=0, 1, . . . , Msymbap−1, of the transmitter precoding operation is defined by the following expression:
                       [                                                                              y                                      (                    0                    )                                                  ⁡                                  (                                      4                    ⁢                    ⅈ                                    )                                                                                                                          y                                      (                    1                    )                                                  ⁡                                  (                                      4                    ⁢                    ⅈ                                    )                                                                                                                          y                                      (                    2                    )                                                  ⁡                                  (                                      4                    ⁢                    ⅈ                                    )                                                                                                                          y                                      (                    3                    )                                                  ⁡                                  (                                      4                    ⁢                    ⅈ                                    )                                                                                                                          y                                      (                    0                    )                                                  ⁡                                  (                                                            4                      ⁢                      ⅈ                                        +                    1                                    )                                                                                                                          y                                      (                    1                    )                                                  ⁡                                  (                                                            4                      ⁢                      ⅈ                                        +                    1                                    )                                                                                                                          y                                      (                    2                    )                                                  ⁡                                  (                                                            4                      ⁢                      ⅈ                                        +                    1                                    )                                                                                                                          y                                      (                    3                    )                                                  ⁡                                  (                                                            4                      ⁢                      ⅈ                                        +                    1                                    )                                                                                                                          y                                      (                    0                    )                                                  ⁡                                  (                                                            4                      ⁢                      ⅈ                                        +                    2                                    )                                                                                                                          y                                      (                    1                    )                                                  ⁡                                  (                                                            4                      ⁢                      ⅈ                                        +                    2                                    )                                                                                                                          y                                      (                    2                    )                                                  ⁡                                  (                                                            4                      ⁢                      ⅈ                                        +                    2                                    )                                                                                                                          y                                      (                    3                    )                                                  ⁡                                  (                                                            4                      ⁢                      ⅈ                                        +                    2                                    )                                                                                                                          y                                      (                    0                    )                                                  ⁡                                  (                                                            4                      ⁢                      ⅈ                                        +                    3                                    )                                                                                                                          y                                      (                    1                    )                                                  ⁡                                  (                                                            4                      ⁢                      ⅈ                                        +                    3                                    )                                                                                                                          y                                      (                    2                    )                                                  ⁡                                  (                                                            4                      ⁢                      ⅈ                                        +                    3                                    )                                                                                                                          y                                      (                    3                    )                                                  ⁡                                  (                                                            4                      ⁢                      ⅈ                                        +                    3                                    )                                                                    ]            =                                                                  1                                  2                                            ⁡                              [                                                                            1                                                              0                                                              0                                                              0                                                              j                                                              0                                                              0                                                              0                                                                                                  0                                                              0                                                              0                                                              0                                                              0                                                              0                                                              0                                                              0                                                                                                  0                                                                                      -                        1                                                                                    0                                                              0                                                              0                                                              j                                                              0                                                              0                                                                                                  0                                                              0                                                              0                                                              0                                                              0                                                              0                                                              0                                                              0                                                                                                  0                                                              1                                                              0                                                              0                                                              0                                                              j                                                              0                                                              0                                                                                                  0                                                              0                                                              0                                                              0                                                              0                                                              0                                                              0                                                              0                                                                                                  1                                                              0                                                              0                                                              0                                                                                      -                        j                                                                                    0                                                              0                                                              0                                                                                                  0                                                              0                                                              0                                                              0                                                              0                                                              0                                                              0                                                              0                                                                                                  0                                                              0                                                              0                                                              0                                                              0                                                              0                                                              0                                                              0                                                                                                  0                                                              0                                                              1                                                              0                                                              0                                                              0                                                              j                                                              0                                                                                                  0                                                              0                                                              0                                                              0                                                              0                                                              0                                                              0                                                              0                                                                                                  0                                                              0                                                              0                                                                                      -                        1                                                                                    0                                                              0                                                              0                                                              j                                                                                                  0                                                              0                                                              0                                                              0                                                              0                                                              0                                                              0                                                              0                                                                                                  0                                                              0                                                              0                                                              1                                                              0                                                              0                                                              0                                                              j                                                                                                  0                                                              0                                                              0                                                              0                                                              0                                                              0                                                              0                                                              0                                                                                                  0                                                              0                                                              1                                                              0                                                              0                                                              0                                                                                      -                        j                                                                                    0                                                                      ]                                      ⁡                          [                                                                                          Re                      ⁡                                              (                                                                              x                                                          (                              0                              )                                                                                ⁡                                                      (                            ⅈ                            )                                                                          )                                                                                                                                                        Re                      ⁡                                              (                                                                              x                                                          (                              1                              )                                                                                ⁡                                                      (                            ⅈ                            )                                                                          )                                                                                                                                                        Re                      ⁡                                              (                                                                              x                                                          (                              2                              )                                                                                ⁡                                                      (                            ⅈ                            )                                                                          )                                                                                                                                                        Re                      ⁡                                              (                                                                              x                                                          (                              3                              )                                                                                ⁡                                                      (                            ⅈ                            )                                                                          )                                                                                                                                                        Im                      ⁡                                              (                                                                              x                                                          (                              0                              )                                                                                ⁡                                                      (                            ⅈ                            )                                                                          )                                                                                                                                                        Im                      ⁡                                              (                                                                              x                                                          (                              1                              )                                                                                ⁡                                                      (                            ⅈ                            )                                                                          )                                                                                                                                                        Im                      ⁡                                              (                                                                              x                                                          (                              2                              )                                                                                ⁡                                                      (                            ⅈ                            )                                                                          )                                                                                                                                                        Im                      ⁡                                              (                                                                              x                                                          (                              3                              )                                                                                ⁡                                                      (                            ⅈ                            )                                                                          )                                                                                                        ]                                ⁢                                          ⁢          for          ⁢                                          ⁢          i                =        0              ,    1    ,    …    ⁢                  ,                            M          symb          layer                -                  1          ⁢                                          ⁢          with          ⁢                                          ⁢                      M            symb            ap                              =              {                                                            4                ⁢                                  M                  symb                  layer                                                                                                      if                  ⁢                                                                          ⁢                                      M                    symb                                          (                      0                      )                                                        ⁢                  mod                  ⁢                                                                          ⁢                  4                                =                0                                                                                                          (                                      4                    ⁢                                          M                      symb                      layer                                                        )                                -                2                                                                                      if                  ⁢                                                                          ⁢                                      M                    symb                                          (                      0                      )                                                        ⁢                  mod                  ⁢                                                                          ⁢                  4                                ≠                0.                                                        
Once again, y(p)(i) indicates the transmitter precoding output signal for antenna p on carrier i as simply permutation and modification of the transmitted symbols x(q)(j). The precoder output feeds the IFFT input in the frequency domain.